Statement A (Assertion) : From a solid cylinder, whose height is … - Vidyadip

MCQ

Statement A (Assertion) : From a solid cylinder, whose height is $12 cm$ and diameter $10 cm$, a conical cavity of same height and same diameter is hollowed out. Then,volume of the cone is $\frac{2200}{7} cm ^3$.
Statement R (Reason) : If a conical cavity of same height and same diameter is hollowed out from a cylinder of height $h$ and base radius $r$, then volume of the cone will be half of the volume of the cylinder.

A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
✓
Assertion $(A)$ is true but reason $(R)$ is false.
D
Assertion (A) is false but reason $(R)$ is true.

✓

Answer

Correct option: C.

Assertion $(A)$ is true but reason $(R)$ is false.

(c) : $\because$ Volume of cylinder $=\pi r^2 h$ and volume of conical cavity $=\frac{1}{3} \pi r^2 h$
$\therefore \quad$ Volume of cone $=\frac{1}{3}$ Volume of cylinder
So, Reason is false.

Now, diameter of cone $=10 cm$
$\therefore \quad$ Radius of cone, $r=5 cm$
Also, height of cone, $h=12 cm$
Volume of cone $=\frac{1}{3} \pi r^2 h$
$
=\frac{1}{3} \times \frac{22}{7} \times 5 \times 5 \times 12=\frac{6600}{21}=\frac{2200}{7} cm ^3
$

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